Name:__________________ Log and Exponent Review

Laws of Logs: Rewrite the exponential equation as a log 1.10x y 2. 43 81 3. 7e x 4. 12xe Use the laws of logarithms to expand the expression

5. 102log ( )xy 6.

2

3logaxyz

§ ·¨ ¸© ¹

7. 3 2ln 3r s 8. 51log1

xx��

Use the laws of logarithms to combine the expression into a single log 9. � �2

5 5log 1 log ( 1)x x� � � 10. ln( ) ln( ) 2lna b a b c� � � � 11. 5 5 52(log 2log 3log )x y z� � Exponent and Log Graphs: Match the graph with the equation

1. 2. 3. A. ( ) 2 3xf x � A. 3( ) log ( 2)f x x � A. ( ) 5 1xf x � B. 3( ) 2xf x � B. 3( ) log ( 2)f x x � B. ( ) 5 1xf x � � C. ( ) 2 3xf x � � C. 3( ) log ( 2)f x x � � C. 5( ) log 1f x x � D. ( ) 2 3xf x � � D. 3( ) log ( 2)f x x � � D. 5( ) log 1f x x � �

4. 5. 6. A. 2( ) log 1f x x � � A. ( ) lnf x x � A. ( ) 3 1xf x � B. 2( ) log 1f x x � B. ( ) ln( )f x x � B. ( ) 3 1xf x � � C. ( ) 2 1xf x � � C. ( ) xf x e� C. 1( ) 3xf x � � D. 1( ) 2xf x � D. ( ) xf x e D. ( ) 3 1xf x � �

Find the domain of the function in interval notation 7. 5( ) log (8 2x)f x � 8 ( ) ln(3 1)f x x � Word Problems: This is the calculator part. Work the word problems from last week that you haven’t done already Solving Log Equations/Exponent Rules:

1. 3416

81

�§ ·¨ ¸© ¹

2. 2 2 7164x x� � 3. 41log2

x � 4. log 8 3x �

5. log 64 3x 6. 2log 2x � 7. 1634

log x 8. log 331

x

9. 4001log 10. 1,000log 11. 4ln e 12. � �102 13. 16log 32 14. � �2log 3 4 3x� 15. � �2log 3 1x x�

16. 271 1log log81 log2 3

x � 17. 5 5 5log 2 3log 2 log 12x � 18. � �3 3log log 8 2x x� �

Solve each equation. Leave your answer in terms of log, ln or e 19. 76x 20. 2 1 53 x� 21. 32 12 7xx �� 22. 2 34 2 14xe � � 23. 4ln( 3) 2 22x � �